Development of Two-Fluid Magnetohydrodynamics Model for Non-Equilibrium Anisotropic Plasma Flows

Abstract

A multi-species magnetohydrodynamic (MHD) model based on an extended fluid dynamics description for each plasma species is proposed for the prediction of the flow and behavior of fully ionized non-equilibrium anisotropic plasmas. In particular, a two-fluid (ions and electrons) plasma model is described that makes use of a 10-moment or Gaussian anisotropic moment closure to model ion and electron species transport. The ion and electron moment equations are fully coupled to the complete set of Maxwell's equations which govern electromagnetic wave propagation within the plasma and a relaxation time approximation is used to model non-equilibrium Coulomb collisional processes between the ions and electrons. Unlike conventional MHD models, the proposed two-fluid model is capable of taking into account large temperature anisotropies and temperature differences between the electrons and ions, both of which can occur for low-density, high-temperature plasmas and/or strongly magnetized plasmas. A dispersion analysis of the proposed model is undertaken in order to examine further its mathematical properties and explore the nature of its solutions. The dispersive and hyperbolic nature of the equations and the disparate times scales or plasma frequencies of the solutions are revealed. The governing system of partial differential equations would appear to be well suited for solution by Godunov-type finite-volume methods provided that the disparate scales can be dealt with. A higherorder finite-volume method is developed here for the solution of the one-dimensional form of the two-fluid plasma model and dispersion analyses of the discretized equations indicates that a stable and practical scheme is possible if a fully implicit time marching scheme is adopted. The analysis also suggests mechanisms for preconditioning the system of equations to further reduce numerical stiffness, resulting in a plasma model that is more suitable for practical applications. Numerical results for several one-dimensional unsteady plasma flows are described and demonstrate the potential of the proposed multi-species plasma model for predicting non-equilibrium anisotropic plasma flows in engineering applications such as those encountered in electric space propulsion devices. The future extension of the model to partially ionized plasmas in two and three space dimensions is also discussed.

Plasma-sheath transition in multi-fluid models with inertial terms under low pressure conditions: Comparison with the classical and kinetic theory

“…Despite the numerical difficulties of multi-fluid models, we have demonstrated that a high-order numerical scheme and the proposed boundary conditions, the simulation is able capture the plasma-sheath transition, being consistent with both the classical and kinetic theories. This work can be extended to more complex multi-fluid models that consider higher-order moments, including non-isotropic tensor [46] which can lead to instabilities at high-temperature sheaths [47]. The importance of writing the equations in conservation form, as opposed to other methods that solve for other nonconserved magnitudes such as velocity and temperature, is fundamental for finite volume methods.…”

Fluid Dynamics, Computational Modeling and Applications

“…This allows for more realistic modelling of the plasma. Presently several efforts are carried out in different countries to develop plasma numerical tools for several applications such as fusion, electric propulsion, active control over hypersonic vehicles: these efforts lead to a growing experience in CMFD field (see Park et al 1999, Kenneth et al 1998, Taku and Atsushi 2004, Cristofolini et al 2007, Miura and Groth 2007, MacCormack 2007, Yalim 2001, Giordano and D'Ambrosio 2004, Battista 2009. The chapter presented was carried out in the context of a research activity motivated by renewed interest in investigating the influence that electromagnetic fields can exert on the thermal and pressure loads imposed on a body invested by a high energetic flow.…”